In this paper we find all solutions of four kinds of the Diophantine equations

begin{equation*}

~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0,

end{equation*}%

for an odd number $t$, and,

begin{equation*}

~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0,

end{equation*}%

for an even number $t$, where $V_{n}$ is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh.

begin{equation*}

~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0,

end{equation*}%

for an odd number $t$, and,

begin{equation*}

~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0,

end{equation*}%

for an even number $t$, where $V_{n}$ is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh.

Type of Study: Research paper |
Subject:
General

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